Boundary Control for a Kind of Coupled PDE-ODE System

A coupled system of an ordinary differential equation (ODE) and a heat partial differential equation (PDE) with spatially varying coefficients is discussed. By using the PDE backstepping method, the state-feedback stabilizing controller is explicitly constructed with the assumptions λ ( x ) ∈ P [ x ] n and λ ( x ) ∈ C [ 0 , l ] ∞ , respectively. The closed-loop system is proved to be exponentially stable by this controller. A simulation example is presented to illustrate the effectiveness of the proposed method.

Abstract licence: CC BY

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